Table 5C.

Atkinson Index

	ε = 0.5			ε = 1.0
	NLS/66	NLSY/79	% Change	NLS/66	NLSY/79	%Change
Factual Economy: Predictable Heterogeneity and Uncertainty1	0.0276	0.0389	0.4111	0.0586	0.0847	0.4446
Counterfactual: Fixing Schooling Choices as in Factual Economy Predictable Heterogeneity Only2	0.0213	0.0286	0.3437	0.0447	0.0604	0.3503
	ε = 1.5			ε = 2.0
	NLS/66	NLSY/79	%Change	NLS/66	NLSY/79	%Change
Factual Economy: Predictable Heterogeneity and Uncertainty1	0.0968	0.1467	0.5147	0.1627	0.2627	0.6149
Counterfactual: Fixing Schooling Choices as in Factual Economy Predictable Heterogeneity Only2	0.0716	0.0980	0.3687	0.1060	0.1506	0.4205

¹

Let Y_k,s,t,i denote the earnings of an agent i, i = 1, …, n_k, at age t, t = 1, …, T, in schooling level s, s = high school, college, and cohort k, k = NLS/1966, NLSY/1979. We model earnings Y_k,s,t,i as:

$$Y_{k,s,t,i}={\mu }_{s,k}\left({\mathit{X}}_k\right)+{\theta }_{1,k,i}{\alpha }_{1,k,s,t,i}+{\theta }_{2,k,i}{\alpha }_{2,k,s,t,i}+{\theta }_{3,k,i}{\alpha }_{3,k,s,t,i}+{\epsilon }_{k,s,t,i}.$$ (i)

The present value of earnings in schooling level s, Y_k,s,i, is $Y_{k,s,i}={\sum }_{t=1}^{T^{\ast }}\frac{Y_{k,s,t,i}}{{(1+\rho )}^{t-1}}$. The observed truncated present value of earnings is Y_k,i = S_k,iY_k,1,i + (1 − S_k,i) Y_k,0,i. Let C_k,i denote the direct costs for individual i in cohort k. The schooling choice is:

$$S_{k,i}=1\iff E(Y_{k,1,i}-Y_{k,0,i}-C_{k,i}\mid {\mathcal{I}}_k)\ge 0.$$ (ii)

This is the factual economy. We then compute the average present value of earnings across all individuals in cohort k, ${\mu }_k=\frac{1}{n}{\sum }_{i=1}^{n_k}{Y}_{k,i}$. For a given inequality aversion parameter ϵ, we compute the level of permanent income ${\stackrel{‒}{Y}}_k\left(ϵ\right)$ that generates the same welfare as the social welfare of the actual distribution in cohort k:

$$\frac{{\left[{\stackrel{‒}{Y}}_k\right(ϵ\left)\right]}^{1-ϵ}-1}{1-ϵ}=\frac{1}{n_k}\sum _{i=1}^{n_k}\frac{{\left(Y_{k,i}\right)}^{1-ϵ}-1}{1-ϵ}$$

For each value of ϵ, the Atkinson Index is $A\left(ϵ\right)=1-\frac{{\stackrel{‒}{Y}}_k\left(ϵ\right)}{{\mu }_k}$. In this row, we show the Atkinson Index for the observed present value of earnings Y_k,i for different values of ϵ.

²

We simulate the economy by replacing (i) with:

$$Y_{k,s,t,i}^h={\mu }_{s,k}\left({\mathit{X}}_k\right)+{\theta }_{1,k,i}{\alpha }_{1,k,s,t,i}+{\theta }_{2,k,i}{\alpha }_{2,k,s,t,i},$$

where $Y_{k,s,t,i}^h$ are the individual earnings when idiosyncratic uncertainty is completely shut down. The present value of earnings when only predictable heterogeneity is accounted for is constructed in a similar manner: $Y_{k,s,i}^h={\sum }_{t=1}^{T^{\ast }}\frac{Y_{k,s,t,i}^h}{{(1+\rho )}^{t-1}}$. The schooling choices are as determined in (ii). In this row, we show the Atkinson Index for the observed present value of earnings $Y_{k,i}^h$ for different values of ϵ when we constrain schooling choices, S_k,i, to be observed in the factual economy.